We present the results of a spectroscopic survey to characterize chromospheric activity, as measured by H{alpha} emission, in low-mass members of the 500Myr old open cluster M37. Combining our new measurements of H{alpha} luminosities (L_H{alpha}_) with previously cataloged stellar properties, we identify saturated and unsaturated regimes in the dependence of the L_H{alpha}_-to-bolometric luminosity ratio, L_H{alpha}_/L_bol_, on the Rossby number R_o_. All rotators with R_o_ smaller than 0.03+/-0.01 converge to an activity level of L_H{alpha}_/L_bol_=(1.27+/-0.02)x10^-4^. This saturation threshold (R_o,sat_=0.03+/-0.01) is statistically smaller than that found in most studies of the rotation-activity relation. In the unsaturated regime, slower rotators have lower levels of chromospheric activity, with L_H{alpha}_/L_bol_(R_o_) following a power-law of index {beta}=-0.51+/-0.02, slightly shallower than that found for a combined ~650Myr old sample of Hyades and Praesepe stars. By comparing this unsaturated behavior to that previously found for coronal activity in M37 (as measured via the X-ray luminosity, L_X_), we confirm that chromospheric activity decays at a much slower rate than coronal activity with increasing R_o_. While a comparison of L_H{alpha}_ and L_X_ for M37 members with measurements of both reveals a nearly 1:1 relation, removing the mass-dependencies by comparing instead L_H{alpha}_/L_bol_ and L_X_/L_bol_ does not provide clear evidence for such a relation. Finally, we find that R_o,sat_ is smaller for our chromospheric than for our coronal indicator of activity (R_o,sat_=0.03+/-0.01 versus 0.09+/-0.01). We interpret this as possible evidence for coronal stripping.